Seismic data acquisition surveys include both land and seabed surveys that utilize seismic receivers arranged in a pattern or grid on either the land or seabed. Seismic sources or seismic shots are created by towing or driving one or more seismic signal generators such as a seismic gun along tow lines or paths, e.g., shot lines. The seismic signal generators are then actuated at multiple locations along the tow lines or paths and the resulting seismic signals are recorded at the seismic receivers on the cables or nodes. The recorded seismic signals are then processed to yield a seismic image of the subsurface below the seismic data acquisition grid.
Seismic images with broad bandwidth are in demand for high resolution imaging of subsurface structures that may lead to more accurate interpretation. However, bandwidth shrinkage of acquired seismic data is present for many reasons including non-uniform attenuation of the medium, free-surface ghost waves, and the bandwidth limitation of the seismic source itself. Many broadband technologies have been developed to address these issues. To remove the free-surface ghost, deghosting technologies have been proposed. Although deghosting can reverse ghost-induced bandwidth shrinkage, deghosting leaves frequency attenuation effects, resulting in slanted spectra with a peak frequency shifted towards the low end.
To compensate for frequency-dependent attenuation, various amplitude Q compensation methods have been proposed. Seismic waves travelling through an attenuative medium experience a loss of energy to that medium via absorption. This absorption affects both the amplitude and phase spectrum of the seismic signal. Moreover, the absorption effect is dispersive, as higher frequencies are more rapidly affected than lower frequencies. The tendency of a particular medium to absorb seismic energy is characterised by its quality factor, Q. This is a dimensionless number, proportional to the fraction of energy lost to the medium per cycle of the seismic wave. In seismic data processing, it is important to compensate for this absorption in order to render an accurate image of the Earth's subsurface reflectivity. Key challenges involved in achieving this include the determination of appropriate Q values for the data in question, as well as implementing the spectral compensation for a given Q in a robust way. However, current methods struggle with a loss in high frequency due to the stabilization requirements of the regularization and the difficulty in obtaining accurate Q models. Moreover, in principle, both deghosting and amplitude Q compensation cannot deal with bandwidth limitation due to the seismic source.
One approach to further enhance resolution is to remove residual source signature and non-stationary Q effects by deconvolution. Deconvolution methods can be classified into two main categories. The first category is filtering-based deconvolution in which a Wiener filter is calculated based on white spectrum reflectivity and minimum phase wavelet assumptions, or minimum entropy of reflectivity assumption, and applied to the seismic traces. However, these methods are very sensitive to parameters in the inverse filter estimation and can amplify noise. The second category is inversion-based deconvolution in which a seismic wavelet is estimated first and the linear convoluting equations are solved as a second inversion problem. Due to the limited bandwidth of the wavelet, deconvolution is an ill-posed problem and regularization is required to overcome the non-uniqueness of the solution.
Compared with traditional L2 regularization that constrains the total energy of the deconvolved trace, sparse regularization gives a simpler and less noisy model that can explain the observations. Performing deconvolution trace-by-trace may introduce inconsistencies and structural non-conformity among neighbouring traces, especially when sparse regularization is used.
In seismic data processing, the phase and amplitude components of the spectral compensation may be applied either simultaneously, or independently at separate stages of the processing sequence (in the latter case, the two components being termed phase-only and amplitude-only Q compensation). Conventional processing flows may, for example, apply the phase correction prior to migration of the data, and the amplitude correction after migration (either pre-stack or post-stack). Alternatively, the Q compensation may be incorporated directly into a Q migration algorithm.
Conventional post-migration amplitude-only Q compensation algorithms typically follow an amplitude damping model. There may be a number of limitations associated with such algorithms. First, an algorithm may not distinguish between seismic signal and background noise, boosting both indiscriminately. Sparse inversion has been proposed as a method for mitigating the influence of noise in Q compensation. Second, an algorithm may be applied only in a 1D sense, which does not guarantee spatial consistency across the geological structures in the seismic data volume. Third, migration shifts spectra to frequencies lower than that of the unmigrated signal in the presence of steep geological dips. A dip-dependent factor has been proposed to correct for this effect. A conventional post-migration Q compensation algorithm may not take this correction factor into account, although a Q migration algorithm may handle steeply dipping events correctly.